Re: Finding derivatives using the product rule

Originally Posted by JellyOnion

I'm having trouble getting the correct answer when using the product rule to find a derivative.

For example when using the product rule to solve ((3x+1)^(3/2))*(2x+4)

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So this is of the form f(x)g(x) with f(x)= (3x+ 1)^(3/2) and g(x)= 2x+ 4.
Of course, the product rule says (fg)'= f'g+ fg'
With f(x)= (3x+ 1)^{3/2}, f'(x)= (3/2)(3x+1)^(1/2)(3)= (9/2)(3x+1)^{1/2} and with g(x)= 2x+ 4, g'(x)= 2.
f'g= (9/2)(3x+1)^{1/2}(2x+ 4) and fg'= 2(3x+1)^{3/2}
[quote]I end up with the answer 9x^(3/2)+18x^(1/2)+6x^(3/2)+2^(3/2)[quote]
You appear to be thinking that (9/2)(3x+ 1)^(1/2)(2x+ 4)= (9/2)[3x^{1/2}+ 4](2x+4) and that 2(3x+1)^{3/2}= 2(3x^{1/2}+ 1).
That is NOT true. In particular, (3x+1)^{3/2} is NOT 3x^(3/2)+ 1.